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fill="currentColor"></path></svg></a></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/algorithms/category/recursion/"><span itemprop="name">Recursion</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Introduction to dynamic programming</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">On this page</button></div><div class="theme-doc-markdown markdown"><header><h1>Introduction to dynamic programming</h1></header><p>In this series we will try to solve one problem in different ways.</p>
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<h2 class="anchor anchorWithStickyNavbar_LWe7" id="problem">Problem<a href="#problem" class="hash-link" aria-label="Direct link to Problem" title="Direct link to Problem"></a></h2>
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<p>The problem we are going to solve is one of <em>CodeWars</em> katas and is called
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<a href="https://www.codewars.com/kata/551f23362ff852e2ab000037" target="_blank" rel="noopener noreferrer">Pyramid Slide Down</a>.</p>
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<p>We are given a 2D array of integers and we are to find the <em>slide down</em>.
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<em>Slide down</em> is a maximum sum of consecutive numbers from the top to the bottom.</p>
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<p>Let's have a look at few examples. Consider the following pyramid:</p>
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<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain"> 3</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 7 4</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 2 4 6</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">8 5 9 3</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
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<p>This pyramid has following slide down:</p>
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<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain"> *3</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> *7 4</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 2 *4 6</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">8 5 *9 3</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
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<p>And its value is <code>23</code>.</p>
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<p>We can also have a look at a <em>bigger</em> example:</p>
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<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain"> 75</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 95 64</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 17 47 82</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 18 35 87 10</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 20 4 82 47 65</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 19 1 23 3 34</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 88 2 77 73 7 63 67</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 99 65 4 28 6 16 70 92</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 41 41 26 56 83 40 80 70 33</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 41 48 72 33 47 32 37 16 94 29</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 53 71 44 65 25 43 91 52 97 51 14</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 70 11 33 28 77 73 17 78 39 68 17 57</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 91 71 52 38 17 14 91 43 58 50 27 29 48</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 63 66 4 68 89 53 67 30 73 16 69 87 40 31</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 4 62 98 27 23 9 70 98 73 93 38 53 60 4 23</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<p>Slide down in this case is equal to <code>1074</code>.</p>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="solving-the-problem">Solving the problem<a href="#solving-the-problem" class="hash-link" aria-label="Direct link to Solving the problem" title="Direct link to Solving the problem"></a></h2>
|
||
<div class="theme-admonition theme-admonition-caution admonition_xJq3 alert alert--warning"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>caution</div><div class="admonitionContent_BuS1"><p>I will describe the following ways you can approach this problem and implement
|
||
them in <em>Java</em><sup><a href="#user-content-fn-1" id="user-content-fnref-1" data-footnote-ref="true" aria-describedby="footnote-label">1</a></sup>.</p></div></div>
|
||
<p>For all of the following solutions I will be using basic <code>main</code> function that
|
||
will output <code>true</code>/<code>false</code> based on the expected output of our algorithm. Any
|
||
other differences will lie only in the solutions of the problem. You can see the
|
||
<code>main</code> here:</p>
|
||
<div class="language-java codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-java codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">public</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">void</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token class-name">String</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token class-name">System</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">out</span><span class="token punctuation" style="color:#393A34">.</span><span class="token function" style="color:#d73a49">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">"Test #1: "</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token class-name">System</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">out</span><span class="token punctuation" style="color:#393A34">.</span><span class="token function" style="color:#d73a49">println</span><span class="token punctuation" style="color:#393A34">(</span><span class="token function" style="color:#d73a49">longestSlideDown</span><span class="token punctuation" style="color:#393A34">(</span><span class="token keyword" style="color:#00009f">new</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">3</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">7</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">4</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">4</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">6</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">8</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">9</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">3</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">23</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">?</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"passed"</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">:</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"failed"</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token class-name">System</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">out</span><span class="token punctuation" style="color:#393A34">.</span><span class="token function" style="color:#d73a49">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">"Test #2: "</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token class-name">System</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">out</span><span class="token punctuation" style="color:#393A34">.</span><span class="token function" style="color:#d73a49">println</span><span class="token punctuation" style="color:#393A34">(</span><span class="token function" style="color:#d73a49">longestSlideDown</span><span class="token punctuation" style="color:#393A34">(</span><span class="token keyword" style="color:#00009f">new</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">75</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">95</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">64</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">17</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">47</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">82</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">18</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">35</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">87</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">10</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">20</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">4</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">82</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">47</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">65</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">19</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">23</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">75</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">3</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">34</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">88</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">77</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">73</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">7</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">63</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">67</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">99</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">65</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">4</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">28</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">6</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">16</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">70</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">92</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">41</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">41</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">26</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">56</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">83</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">40</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">80</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">70</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">33</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">41</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">48</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">72</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">33</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">47</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">32</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">37</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">16</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">94</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">29</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">53</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">71</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">44</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">65</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">25</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">43</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">91</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">52</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">97</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">51</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">14</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"> </span><span class="token number" 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class="token number" style="color:#36acaa">98</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">73</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">93</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">38</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">53</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">60</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">4</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">23</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1074</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">?</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"passed"</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">:</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"failed"</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" 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